The basis of this work was, essentially, vague annoyance. A lot of our previous work used time-frequency entanglement, where the time and color correlations between photon pairs are incompatible with classical statistics, but infuriatingly, the measurements we made could be potentially described with classical statistics. We manipulated the frequency correlations, but couldn’t measure the time correlations at the same time. We violated Bell inequalities with time measurements, but it relied on converting one of the two measurement steps to a polarization measurement. There have been plenty of demonstrations proving time-frequency entanglement through nonlocal interference effects and measuring the structure by using analogies with classical nonlinear processes, but we just wanted to see it dammit!

So that’s what we did, and it looks like this:

We used a standard bulk-optics downconversion source, and set up two apparatuses. One was a simple scanning spectrometer that mapped out the frequency range, the other was a sum-frequency process gated by an ultrashort (sub-picosecond) laser pulse. The key to these techniques, which for the record are essentially the most brute-force techniques available for these tasks, is that they allow us to measure with photon detectors on both sides (i.e. so we can measure the photon pair in coincidence) and that their resolutions in time and frequency are *just* compatible enough with our photon pair source. Whereas most single-photon time measurement techniques aren’t fast enough to measure these correlations, when the photon timescales are large enough to measure, then the standard frequency measurement techniques cease to work.

By operating in that sweet spot, we were able to explicitly show the anti-correlations in frequency (arising from the fact that the two photons must together add up to the pump energy) and the correlations in time-of-arrival (since the two photons must be created at the same time) with the same source. Using this data, we were able to violate the EPR uncertainty relation, originally proposed in the context of space and momentum, for the first time in this domain. But really, the important part is we experimentally obtained a very pretty picture, and can now sleep easier about what time-frequency entanglement looks like.